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On the probability that two random integers are coprimeMay 31 2018We provide rigorous probability interpretations of the statement "the probability that two random integers are co-prime is $6/\pi^2$". In order to properly define a "uniform" probability measure on natural numbers, we consider two settings. In the first ... More

Global and Local Two-Sample Tests via RegressionDec 21 2018Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature, there have been ... More

Disk-Evaporation Fed Corona: Structure and Evaporation Feature with Magnetic FieldJul 03 2007The disk-corona evaporation model naturally interprets many observational phenomena in black hole X-ray binaries, such as the truncation of an accretion disk and the spectral state transitions. On the other hand, magnetic field is known to play an important ... More

Antenna Current Optimization and Realizations for Far-Field Pattern ShapingNov 27 2017Aug 24 2018Far-field shaping of small antennas is a challenge and the realizations of non-dipole radiation of small to intermediate sized antennas are difficult. Here we examine the antenna bandwidth cost associated with such constraints, and in certain cases we ... More

Dynamics of drying in 3D porous mediaJul 29 2008The drying dynamics in three dimensional porous media are studied with confocal microscopy. We observe abrupt air invasions in size from single particle to hundreds of particles. We show that these result from the strong flow from menisci in large pores ... More

Full counting statistics of phonon-assisted Andreev tunneling through a quantum dot coupled to normal and superconducting leadsNov 10 2016Dec 27 2016We present a theoretical investigation for the full counting statistics of the Andreev tunneling through a quantum dot (QD) embedded between superconducting (SC) and normal leads in the presence of a strong on-site electron-phonon interaction using nonequilibrium ... More

Spin glass in semiconducting KFe$_{1.05}$Ag$_{0.88}$Te$_{2}$ single crystalsApr 20 2016We report discovery of KFe$_{1.05}$Ag$_{0.88}$Te$_{2}$ single crystals with semiconducting spin glass ground state. Composition and structure analysis suggest nearly stoichiometric I4/mmm space group but allow for the existence of vacancies, absent in ... More

Search for the Signatures of a New-Born Black Hole from the Collapse of a Supra-massive Millisecond Magnetar in Short GRB Light CurvesDec 12 2017`Internal plateau' followed by a sharp decay is commonly seen in short gamma-ray burst (GRB) light curves. The plateau component is usually interpreted as the dipole emission from a supra-massive magnetar, and the sharp decay may imply the collapse of ... More

THEMIS Observations of the Magnetopause Electron Diffusion Region: Large Amplitude Waves and Heated ElectronsJan 16 2013We present the first observations of large amplitude waves in a well-defined electron diffusion region at the sub-solar magnetopause using data from one THEMIS satellite. These waves identified as whistler mode waves, electrostatic solitary waves, lower ... More

$K^*$ mesons with hidden charm arising from $KX(3872)$ and $KZ_c(3900)$ dynamicsMay 22 2018Aug 23 2018Inspired by the recent discovery of the pentaquark states $P_c(4450)$ and $P_c(4380)$, which can be viewed as excited nucleon states with hidden charm, we study the three-body interaction of a kaon and a pair of $D\bar{D}^*$ in isospin 0 and 1. We show ... More

A model of the light curves of Gamma-Ray BurstsMar 10 2007Mar 27 2007An extreme Kerr black hole (BH) surrounded by a precessing disk is invoked to explain the light curves of gamma-ray bursts (GRBs) based on the coexistence of the Blandford-Znajek (BZ) and the magnetic coupling (MC) processes. The overall shape of the ... More

Physical properties of KxNi2-ySe2 single crystalsNov 06 2012We have synthesized K0.95(1)Ni1.86(2)Se2 single crystals. The single crystals contain K and Ni deficiencies not observed in KNi2Se2 polycrystals. Unlike KNi2Se2 polycrystals, the superconductivity is absent in single crystals. The detailed physical property ... More

Structure and physical properties of new layered iron oxychalcogenide BaFe2OSe2Jun 25 2012We have successfully synthesized a new layered iron oxychalcogenide BaFe2OSe2 single crystal. This compound is built up of Ba and Fe-Se(O) layers alternatively stacked along the c-axis. The Fe-Se(O) layers contain double chains of edge-shared Fe-Se(O) ... More

Extremal problems on saturation for the family of $k$-edge-connected graphsOct 20 2017Mar 03 2018Let $\mathcal{F}$ be a family of graphs. A graph $G$ is $\mathcal{F}$-saturated if $G$ contains no member of $\mathcal{F}$ as a subgraph but $G+e$ contains some member of $\mathcal{F}$ whenever $e\in E(\overline{G})$. The saturation number and extremal ... More

Superconductivity in Ir1-xRhxTe2 (0<=x<=0.3)Jul 26 2013We report superconductivity, physical and structural properties of Ir1-xRhxTe2 (0<=x<=0.3). Superconducting transition with maximum Tc~2.6 K appears when the doping content of Rh x is in between 0.15 and 0.3. Further increasing the content of Rh will ... More

Is silicene stable in air? -- First principles study of oxygen adsorption and dissociation on siliceneOct 25 2013The oxygen adsorption and dissociation on pristine silicene surface are studied by use of first-principles in this letter. The oxygen adsorption and dissociation on pristine silicene surface are studied by use of first-principles in this letter. It is ... More

Effects of excess Fe on upper critical field and magnetotransport in Fe1+y(Te1-xSx)zMar 10 2010We have investigated the upper critical field anisotropy and magnetotransport properties of Fe1.14(1)Te0.91(2)S0.09(2) single crystals in stable magnetic fields up to 35 T. The results show that u0Hc2(T) along the c axis and in the ab-plane exhibit saturation ... More

Pauli-limited upper critical field in Fe1+yTe1-xSexJan 11 2010Mar 10 2010In this work we investigated the temperature dependence of the upper critical field u0Hc2(T) of Fe1.02(3)Te0.61(4)Se0.39(4) and Fe1.05(3)Te0.89(2)Se0.11(2) single crystals by measuring the magnetotransport properties in stable dc magnetic fields up to ... More

Load Balancing via Joint Transmission in Heterogeneous LTE: Modeling and ComputationFeb 26 2016As one of the Coordinated Multipoint (CoMP) techniques, Joint Transmission (JT) can improve the overall system performance. In this paper, from the load balancing perspective, we study how the maximum load can be reduced by optimizing JT pattern that ... More

Range Assignment for Power Optimization in Load-Coupled Heterogeneous NetworksFeb 26 2016We consider the problem of transmission energy op- timization via range assignment for Low Power Nodes (LPNs) in Long Term Evolution (LTE) Heterogenous Networks (HetNets). The optimization is subject to the load coupling model, where the cells interfere ... More

Constraining Photon Mass by Energy-Dependent Gravitational Light BendingJun 06 2014In the standard model of particle physics, photons are mass-less particles with a particular dispersion relation. Tests of this claim at different scales are both interesting and important. Experiments in territory labs and several exterritorial tests ... More

Equidistribution of expanding curves in homogeneous spaces and Diophantine approximation for square matricesNov 05 2013Nov 08 2015In this article, we study an analytic curve $\varphi: I=[a,b]\rightarrow \mathrm{M}(n\times n, \mathbb{R})$ in the space of $n$ by $n$ real matrices, and show that if $\varphi$ satisfies certain geometric conditions, then for almost every point on the ... More

Quasi-periodic Almost-collision Orbits in the Spatial Three-Body ProblemAug 12 2013In a system of particles, quasi-periodic almost-collision orbits are collisionless orbits along which two bodies become arbitrarily close to each other -- the lower limit of their distance is zero but the upper limit is strictly positive -- and which ... More

Nonlinear differential Galois theoryAug 20 2006Apr 23 2011Differential Galois theory has played important roles in the theory of integrability of linear differential equation. In this paper we will extend the theory to nonlinear case and study the integrability of the first order nonlinear differential equation. ... More

Calculation of l-adic local Fourier transformationsFeb 15 2007Jun 04 2010We calculate the local Fourier transformations for a class of $\bar{\mathbb Q}_\ell$-sheaves. In particular, we verify a conjecture of Laumon and Malgrange. As an application, we calculate the local monodromy of $\ell$-adic hypergeometric sheaves introduced ... More

$Sp_{2n}(F_{q^{2}})$-Invariants In Irreducible Unipotent Representations of $Sp_{4n}(F_{q})$Mar 28 2013We show that for any irreducible representation of $Sp_{4n}(F_{q})$, the subspace of all its $Sp_{2n}(F_{q^{2}})$-invariants is at most one-dimensional. In terms of Lusztig symbols, we give a complete list of irreducible unipotent representations of $Sp_{4n}(F_{q})$ ... More

Galois representations arising from twenty-seven lines on a cubic surface and the arithmetic associated with Hessian polyhedraDec 14 2006In the present paper, we will show that three apparently disjoint objects: Galois representations arising from twenty-seven lines on a cubic surface (number theory and arithmetic algebraic geometry), Picard modular forms (automorphic forms), rigid Calabi-Yau ... More

Bounds on the Tamagawa numbers of a crystalline representation over towers of cyclotomic extensionsOct 21 2015In this paper, we study the Tamagawa numbers of a crystalline representation over a tower of cyclotomic extensions under certain technical conditions on the representation. In particular, we show that we may improve the asymptotic bounds given in the ... More

$\ell$-adic GKZ hypergeometric sheaf and exponential sumsAug 07 2012Apr 26 2016To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the $\ell$-adic counterpart of the ... More

A fast spectral method for the Uehling-Uhlenbeck equation for quantum gas mixtures: homogeneous relaxation and transport coefficientsOct 07 2018A fast spectral method (FSM) is developed to solve the Uehling-Uhlenbeck equation for quantum gas mixtures with generalized differential cross-sections. Spatially-homogeneous relaxation problems are used to demonstrate that the FSM conserves mass and ... More

Vanishing estimates for fully bubbling solutions of $SU(n+1)$ Toda Systems at a singular sourceApr 20 2018For Gauss curvature equation (or more general Toda systems) defined on two dimensional spaces, the vanishing rate of certain curvature functions on blowup points is a key estimate for numerous applications. However, if these equations have singular sources, ... More

Asymptotic Behavior of Blowup Solutions for Elliptic Equations with Exponential Nonlinearity and Singular DataOct 28 2008We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello it ... More

Small trees in supercritical random forestsOct 07 2017We study the scaling limit of random forest with prescribed degree sequence in the regime that the largest tree consists of all but a vanishing fraction of nodes. We give a description of the limit of the forest consisting of the small trees, by relating ... More

Scaling limit of random forests with prescribed degree sequencesApr 07 2017In this paper, we consider the random plane forest uniformly drawn from all possible plane forests with a given degree sequence. Under suitable conditions on the degree sequences, we consider the limit of a sequence of such forests with the number of ... More

Exotic arithmetic structure on the first Hurwitz tripletSep 09 2012May 21 2013We find that the first Hurwitz triplet possesses two distinct arithmetic structures. As Shimura curves $X_1$, $X_2$, $X_3$, whose levels are with norm 13. As non-congruence modular curves $Y_1$, $Y_2$, $Y_3$, whose levels are 7. Both of them are defined ... More

Section problems for configuration spaces of surfacesAug 26 2017Jul 30 2018In this paper we give a close-to-sharp answer to the basic questions: When is there a continuous way to add a point to a configuration of $n$ ordered points on a surface $S$ of finite type so that all the points are still distinct? When this is possible, ... More

On the non-realizability of braid groups by homeomorphismsAug 24 2018In this paper, we will show that the projection $\text{Homeo}^+(D^2_n)\to B_n$ does not have a section; i.e. the braid group $B_n$ cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary point-wise and $n$ marked points ... More

Abundance of non-uniruled 3-folds with non-trivial Albanese maps in positive characteristicsOct 12 2016In this paper, we prove abundance for non-uniruled 3-folds with non-trivial Albanese maps, over an algebraically closed field of characteristic $p > 5$. As an application we get a characterization of abelian 3-folds.

Trace formulas for a class of compact complex surfacesAug 27 2001We give the trace formulas of weight $k$ for cocompact, torsion-free discrete subgroups of $SU(2, 1)$ and prove the analogue of the Riemann hypothesis on compact complex surfaces $M$ with $c_1^2(M)=3 c_2(M)$, where $c_i(M)$ is the $i$-th Chern class of ... More

A note on Perelman's LYH inequalityFeb 15 2006We give a proof to the Li-Yau-Hamilton type inequality claimed by Perelman on the fundamental solution to the conjugate heat equation. The rest of the paper is devoted to improving the known differential inequalities of Li-Yau-Hamilton type via monotonicity ... More

Dedekind $η$-function, Hauptmodul and invariant theoryJul 14 2014Aug 18 2014We solve a long-standing open problem with its own long history dating back to the celebrated works of Klein and Ramanujan. This problem concerns the invariant decomposition formulas of the Hauptmodul for $\Gamma_0(p)$ under the action of finite simple ... More

Non-commutative p-adic L-functions for supersingular primesJan 05 2012Jun 06 2012Let E/Q be an elliptic curve with good supersingular reduction at p with a_p(E)=0. We give a conjecture on the existence of analytic plus and minus p-adic L-functions of E over the Zp-cyclotomic extension of a finite Galois extension of Q where p is unramified. ... More

Equidistribution of expanding translates of curves in homogeneous spaces with the action of $(\mathrm{SO}(n,1))^k$Jun 04 2017Given a homogeneous space $X = G/\Gamma$ with $G$ containing the group $H = (\mathrm{SO}(n,1))^k$. Let $x\in X$ such that $Hx$ is dense in $X$. Given an analytic curve $\phi: I=[a,b] \rightarrow H$, we will show that if $\phi$ satisfies certain geometric ... More

Beyond the Central Limit Theorem: Universal and Non-universal Simulations of Random Variables by General MappingsAug 06 2018Dec 04 2018Motivated by the Central Limit Theorem, in this paper, we study both universal and non-universal simulations of random variables with an arbitrary target distribution $Q_{Y}$ by general mappings, not limited to linear ones (as in the Central Limit Theorem). ... More

Deformation of $\ell$-adic sheaves with Undeformed Local MonodromyMar 06 2011Sep 29 2012Let $X$ be a smooth connected algebraic curve over an algebraically closed field $k$. We study the deformation of $\ell$-adic Galois representations of the function field of $X$ while keeping the local Galois representations at all places undeformed.

On Conditional CorrelationsNov 09 2018The Pearson correlation, correlation ratio, and maximal correlation have been well-studied in the literature. In this paper, we studied the conditional versions of these quantities. We extend the most important properties of the unconditional versions ... More

Blowup solutions of elliptic systems in two dimensional spacesNov 04 2013This is the content of the talk the author gave in the section of partial differential equations at the International Congress of Chinese Mathematicians, 2013, Taipei.

Icosahedron, exceptional singularities and modular formsNov 17 2015We find that the equation of $E_8$-singularity possesses two distinct symmetry groups and modular parametrizations. One is the classical icosahedral equation with icosahedral symmetry, the associated modular forms are theta constants of order five. The ... More

A Generalized Krein-Rutman TheoremJun 14 2016A generalized Krein-Rutman theorem for a strongly positive bounded linear operator whose spectral radius is larger than essential spectral radius is established: the spectral radius of the operator is an algebraically simple eigenvalue with strongly positive ... More

Surjective homomorphisms between surface braid groupsApr 17 2017Let $PB_n(S_{g,p})$ be the pure braid group of a genus $g>1$ surface with $p$ punctures. In this paper we prove that any surjective homomorphism $PB_n(S_{g,p})\to PB_m(S_{g,p})$ factors through one of the forgetful homomorphisms. We then compute the automorphism ... More

Factorisation of two-variable p-adic L-functionsApr 28 2013Let $f$ be a modular form which is non-ordinary at $p$. Kim and Loeffler have recently constructed two-variable $p$-adic $L$-functions associated to $f$. In the case where $a_p=0$, they showed that, as in the one-variable case, Pollack's plus and minus ... More

On the Rate of Convergence of Mean-Field Models: Stein's Method Meets the Perturbation TheoryOct 03 2015This paper studies the rate of convergence of a family of continuous-time Markov chains (CTMC) to a mean-field model. When the mean-field model is a finite-dimensional dynamical system with a unique equilibrium point, an analysis based on Stein's method ... More

A goodness-of-fit test for stochastic block modelsDec 16 2014Jan 21 2016The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix obtained by ... More

The fundamental group, rational connectedness and the positivity of Kaehler manifoldsFeb 03 2019First a conjecture asserting that any compact K\"ahler manifold $N$ with $Ric^\perp>0$ must be simply-connected is confirmed by adapting the comass of $(p, 0)$-forms into a maximum principle via the viscosity consideration. Secondly the projectivity and ... More

Representations of Lie superalgebras in prime characteristic IIIOct 12 2009For a restricted Lie superalgebra g over an algebraically closed field of characteristic p > 2, we generalize the deformation method of Premet and Skryabin to obtain results on the p-power and 2-power divisibility of dimensions of g-modules. In particular, ... More

l-adic realization of some aspect of Landau-Ginzburg B-modelsMar 10 2017The Landau-Ginzburg B-model for a germ of a holomorphic function with an isolated critical point is constructed by K. Saito and finished by M. Saito. Douai and Sabbah construct the Landau-Ginzburg B-models for some Laurent polynomials. The construction ... More

Product formulas on a unitary group in three variablesApr 27 2001Apr 30 2001We obtain some basic partial differential operators connected with nonholomorphic automorphic forms on $\Gamma \backslash U(2, 1)/K$. We give the corresponding Eisenstein series of weight $k$ and automorphic Green functions of weight $k$. Moreover, we ... More

Hausdorff dimension of divergent diagonal geodesics on product of finite volume hyperbolic spacesMar 24 2013Nov 08 2015In this article, we consider the product space of several non-compact finite volume hyperbolic spaces, $V_1, V_2, \dots , V_k$ of dimension $n$. Let $\mathrm{T}^1(V_i)$ denote the unit tangent bundle of $V_i$ for each $i=1,\dots , k$, then for every $(v_1, ... More

Hessian polyhedra, invariant theory and Appell hypergeometric partial differential equationsDec 03 2004Dec 16 2004It is well-known that Klein's lectures on the icosahedron and the solution of equations of fifth degree is one of the most important and influential books of 19th-century mathematics. In the present paper, we will give the complex counterpart of Klein's ... More

Estimating class numbers over metabelian extensionsMar 30 2017Let $p$ be an odd prime and $L/K$ a $p$-adic Lie extension whose Galois group is of the form $\mathbb{Z}_p^{d-1}\rtimes \mathbb{Z}_p$. Under certain assumptions on the ramification of $p$ and the structure of an Iwasawa module associated to $L$, we study ... More

Coleman Maps for Modular Forms at Supersingular Primes over Lubin-Tate ExtensionsAug 01 2009Jul 12 2010Given an elliptic curve with supersingular reduction at an odd prime p, Iovita and Pollack have generalised results of Kobayashi to define even and odd Coleman maps at p over Lubin-Tate extensions given by a formal group of height 1. We generalise this ... More

The cohomological support locus of pluricaonical sheaves and the Iitaka fibrationDec 16 2012Nov 28 2013Let $alb_X: X \rightarrow A$ be the Albanese map of a smooth projective variety and $f: X \rightarrow Y$ the fibration from the Stein factorization of $alb_X$. For a positive integer $m$, if $f$ and $m$ satisfy the assumptions AS(1,2), then the translates ... More

New Conserved Quantities of the Incompressible Euler EquationsJul 30 2010Aug 03 2010We show two new conserved quantities for the three-dimensional incompressible Euler equations. Due to professor Lin's comments, these quantities are deeply related to the concept of topological degree and not new. I will post a new version soon.

Deformations and Rigidity of $\ell$-adic SheavesNov 12 2016May 10 2018Let $X$ be a smooth connected projective algebraic curve over an algebraically closed field, and let $S$ be a finite nonempty closed subset in $X$. We study deformations of $\overline{\mathbb F}_\ell$-sheaves. The universal deformation space is a formal ... More

A short note on doubly substochastic analog of Birkhoff's theoremJan 04 2018Let B be an n by n doubly substochastic matrix. We show that B can be written as a convex combination of no more than {\sigma}(B)+t subpermutation matrices, where {\sigma}(B) is the number of nonzero elements in B and t is the number of fully indecomposable ... More

A new conception for computing gröbner basis and its applicationsDec 24 2010Dec 28 2010This paper presents a conception for computing gr\"{o}bner basis. We convert some of gr\"{o}bner-computing algorithms, e.g., F5, extended F5 and GWV algorithms into a special type of algorithm. The new algorithm's finite termination problem can be described ... More

Badly approximable points on curves and unipotent orbits in homogeneous spacesMar 09 2017In this paper, we study the weighted $n$-dimensional badly approximable points on curves. Given an analytic non-degenerate curve $\varphi: I= [a,b] \to \mathbb{R}^n$, we will show that any countable intersection of the sets of the weighted badly approximable ... More

The number of fiberings of a surface bundle over a surfaceMar 20 2017For a closed manifold $M$, let Fib$(M)$ be the number of distinct fiberings of $M$ as a fiber bundle with fiber a closed surface. In this paper we give the first computation of Fib$(M)$ where $1<\text{Fib}(M)<\infty$ but $M$ is not a product. In particular, ... More

The Exterior Cubic L-function of GU(6) and Unitary Automorphic InductionMar 11 2019In this paper, we extend Ginzburg-Rallis' integral representation for the exterior cube automorphic $L$-function of ${\rm GL}_6\times {\rm GL}_1$ to that of the quasi-split unitary similitude group ${\rm GU}_6$ and establish its analytic properties to ... More

Partial Reduction and Delaunay/Deprit VariablesJan 23 2014Jul 12 2014Based on a concept link between the partial reduction procedure of the reduction of the rotational symmetry of the N-body problem with the symplectic cross-section theorem of Guillemin-Sternberg, we present alternative proofs of the symplecticity of Delaunay ... More

Collisionless Magnetic Reconnection via Alfven EigenmodesJul 04 2009We propose an analytic approach to the problem of collisionless magnetic reconnection formulated as a process of Alfven eigenmodes' generation and dissipation. Alfven eigenmodes are confined by the current sheet in the same way that quantum mechanical ... More

Geometry and arithmetic associated to Appell hypergeometric partial differential equationsSep 25 2003Dec 16 2004In this paper, we study the monodromy of Appell hypergeometric partial differential equations, which lead us to find four derivatives which are associated to the group GL(3). Our four derivatives have the remarkable properties. We find that Appell hypergeometric ... More

Poincaré series and modular functions for U(n, 1)May 02 2001We construct infinitely many nonholomorphic automorphic forms and modular forms associated to a discrete subgroup of infinite covolume of $U(n, 1)$.

Tackling Sequence to Sequence Mapping Problems with Neural NetworksOct 25 2018In Natural Language Processing (NLP), it is important to detect the relationship between two sequences or to generate a sequence of tokens given another observed sequence. We call the type of problems on modelling sequence pairs as sequence to sequence ... More

The sharp lower bound for the volume of 3-folds of general type with χ(\Co{X})=1Oct 24 2007Let $V$ be a smooth projective 3-fold of general type. Denote by $K^{3}$, a rational number, the self-intersection of the canonical sheaf of any minimal model of $V$. One defines $K^{3}$ as a canonical volume of $V$. The paper is devoted to proving the ... More

Thresholding for Top-k Recommendation with Temporal DynamicsJun 06 2015Nov 09 2015This work focuses on top-k recommendation in domains where underlying data distribution shifts overtime. We propose to learn a time-dependent bias for each item over whatever existing recommendation engine. Such a bias learning process alleviates data ... More

Dictionary for Sparse Representation of Chirp Echo in Broadband RadarAug 01 2010Aug 03 2010A new dictionary for sparse representation of chirp echo in broadband radar is put forward in this paper. Different with chirplet decomposition which decomposes echo in time-frequency plane, the dictionary transforms the sparsity of target observed by ... More

Iwasawa Theory for the Symmetric Square of a CM Modular Form at Inert PrimesDec 08 2010Aug 16 2011Let f be a CM modular form and p an odd prime which is inert in the CM field. We construct two p-adic L-functions for the symmetric square of f, one of which has the same interpolating properties as the one constructed by Delbourgo-Dabrowski, whereas ... More

Iwasawa Theory for Modular Forms at Supersingular PrimesApr 24 2009Jul 21 2010We generalise works of Kobayashi to give a formulation of the Iwasawa main conjecture for modular forms at supersingular primes. In particular, we give analogous definitions of even and odd Coleman maps for normalised new forms of arbitrary weights and ... More

Vanishing and injectivity for R-Hodge modules and R-divisorsSep 10 2018We prove the injectivity and vanishing theorem for R-Hodge modules and R-divisors over projective varieties, extending the results for rational Hodge modules and integral divisors in \cite{Wu15}. In particular, the injectivity generalizes the fundamental ... More

Modular curves, invariant theory and $E_8$Apr 06 2017Jun 08 2017The $E_8$ root lattice can be constructed from the modular curve $X(13)$ by the invariant theory for the simple group $\text{PSL}(2, 13)$. This gives a different construction of the $E_8$ root lattice. It also gives an explicit construction of the modular ... More

Prescribing curvatures on three dimensional Riemannian manifolds with boundariesOct 28 2008Let $(M,g)$ be a complete three dimensional Riemannian manifold with boundary $\partial M$. Given smooth functions $K(x)>0$ and $c(x)$ defined on $M$ and $\partial M$, respectively, it is natural to ask whether there exist metrics conformal to $g$ so ... More

A priori estimate for a family of semi-linear elliptic equations with critical nonlinearityOct 28 2008We consider positive solutions of $\Delta u-\mu u+Ku^{\frac{n+2}{n-2}}=0$ on $B_1$ ($n\ge 5$) where $\mu $ and $K>0$ are smooth functions on $B_1$. If $K$ is very sub-harmonic at each critical point of $K$ in $B_{2/3}$ and the maximum of $u$ in $\bar ... More

The universal $n$-pointed surface bundle only has $n$ sectionsNov 14 2016Sep 02 2018The classifying space BDiff$(S_{g,n})$ of the orientation-preserving diffeomorphism group of the surface $S_{g,n}$ of genus $g>1$ with $n$ ordered marked points has a universal bundle \[ S_g \to \text{UDiff}(S_{g,n})\xrightarrow{\pi}\text{BDiff}(S_{g,n}). ... More

The universal surface bundle over the Torelli space has no sectionsOct 02 2017Oct 09 2017For $g>3$, we give two proofs of the fact that the \emph{Birman exact sequence} for the Torelli group \[ 1\to \pi_1(S_g)\to {\cal I}_{g,1}\to {\cal I}_g\to 1 \] does not split. This result was claimed by G. Mess in \cite{mess1990unit}, but his proof has ... More

Device-to-Device Load Balancing for Cellular NetworksOct 07 2017Dec 12 2018Small-cell architecture is widely adopted by cellular network operators to increase network capacity. By reducing the size of cells, operators can pack more (low-power) base stations in an area to better serve the growing demands, without causing extra ... More

Drying of complex suspensionsMar 31 2010We investigate the 3D structure and drying dynamics of complex mixtures of emulsion droplets and colloidal particles, using confocal microscopy. Air invades and rapidly collapses large emulsion droplets, forcing their contents into the surrounding porous ... More

Intertwined magnetic and nematic orders in semiconducting KFe$_{0.8}$Ag$_{1.2}$Te$_2$Jan 31 2019Superconductivity in the iron pnictides emerges from metallic parent compounds exhibiting intertwined stripe-type magnetic order and nematic order, with itinerant electrons suggested to be essential for both. Here we use X-ray and neutron scattering to ... More

Broken Time Reversal Symmetry in Superconducting Pr1-xCexPt4Ge12Mar 13 2015We report results of zero-field muon spin relaxation experiments on the filled-skutterudite superconductors~Pr$_{1-x}$Ce$_{x}$Pt$_4$Ge$_{12}$, $x = 0$, 0.07, 0.1, and 0.2, to investigate the effect of Ce doping on broken time-reversal symmetry (TRS) in ... More

Gamma-Ray Burst in a Molecular Cloud: Destruction of Dust and H2, and Emergent SpectrumAug 14 2001A gamma ray burst with strong optical-UV emission occuring in a molecular cloud will photodissociate H2, photoionize H2, H, and He, and destroy dust grains. We model these processes, including time-dependent radiative transfer in both continuum radiation ... More

Evolution of cross-correlation and time lag of Cyg X-2 along the branchesJan 22 2008We report the detections of the anti-correlated soft and hard X-rays, and the time lags of $\sim$ hecto-second from the neutron star low-mass X-ray binary Cyg X-2, a well-known Z-type luminous source. Both the anti-correlation and the positive correlation ... More

Determining temperature and Rabi frequency regarding trapped ions in Doppler cooling: An analytic investigationFeb 01 2019Doppler cooling with lasers is essential to ions' trapping and also a preliminary step towards achievement of ultracold ions. Due to lack of effective tools, experimentally monitoring the ions' temperature and the laser-ion coupling is difficult in Doppler ... More

Tuning phase transitions of FeSe thin flakes by field effect transistor with solid ion conductor as gate dielectricSep 25 2016We develop a novel field effect transistor (FET) device using solid ion conductor (SIC) as a gate dielectric, and we can tune the carrier density of FeSe by driving lithium ions in and out of the FeSe thin flakes, and consequently control the material ... More

Convergence of Unregularized Online Learning AlgorithmsAug 09 2017In this paper we study the convergence of online gradient descent algorithms in reproducing kernel Hilbert spaces (RKHSs) without regularization. We establish a sufficient condition and a necessary condition for the convergence of excess generalization ... More

An In-Vehicle KWS System with Multi-Source Fusion for Vehicle ApplicationsFeb 12 2019Feb 17 2019In order to maximize detection precision rate as well as the recall rate, this paper proposes an in-vehicle multi-source fusion scheme in Keyword Spotting (KWS) System for vehicle applications. Vehicle information, as a new source for the original system, ... More

Morphology of AGN Emission Line Regions in SDSS-IV MaNGA SurveyMay 17 2018Nov 11 2018Extended narrow-line regions (NLRs) around active galactic nuclei (AGN) are shaped by the distribution of gas in the host galaxy and by the geometry of the circumnuclear obscuration, and thus they can be used to test the AGN unification model. In this ... More

Phase diagram and physical properties of NaFe$_{1-x}$Cu$_x$As single crystalsJul 23 2013A series of high quality NaFe$_{1-x}$Cu$_x$As single crystals has been grown by a self-flux technique, which were systematically characterized via structural, transport, thermodynamic, and high pressure measurements. Both the structural and magnetic transitions ... More

High-Tc superconductivity up to 55 K under high pressure in the heavily electron doped Lix(NH3)yFe2Se2 single crystalSep 25 2017We report a high-pressure study on the heavily electron doped Lix(NH3)yFe2Se2 single crystal by using the cubic anvil cell apparatus. The superconducting transition temperature Tc = 44 K at ambient pressure is first suppressed to below 20 K upon increasing ... More

Local structure and Fe-vacancy disorder to order crossover in K$_x$Fe$_{2-y}$Se$_{2-z}$S$_z$Feb 28 2019The detailed account of the local atomic structure and structural disorder at 5~K across the phase diagram of K$_x$Fe$_{2-y}$Se$_{2-z}$S$_z$ $(0 \leq z \leq 2)$ high temperature superconductor is obtained from neutron total scattering and associated atomic ... More

A new variable for SRS plan quality evaluation based on normal tissue sparing: The Effect of Prescription Isodose LevelsAug 27 2014Objectives: A new dosimetric variable, dose dropping speed (DDS), was proposed and used to evaluate normal tissue sparing among stereotactic radiosurgery (SRS) plans with different prescription isodose lines. Methods: Forty plans were generated for 8 ... More